note gumby I was waiting for another one of these posts ;-) Rule 90 will generate Sierpinski's sieve (but then, you can in turn generate that from Pascal's triangle (mod 2)).<p> <code> #!/usr/bin/perl -w use strict; my (\$file, %rules, \$string, \$rewrite, \$angle, \$i); \$file = "gosper"; # Peano-Gosper curve. \$rules{"X"} = "X+YF++YF-FX--FXFX-YF+"; \$rules{"Y"} = "-FX+YFYF++YF+FX--FX-Y"; \$string = "FX"; \$angle = 60; \$i = 4; foreach (1..\$i) { \$rewrite = ""; for (split //,\$string) { \$rewrite .= \$rules{\$_} || \$_; } \$string = \$rewrite; } open PS,">\$file.ps"; print PS "%#\n\n"; print PS "306 396 moveto\n"; for my \$ch (split //,\$string) { if (\$ch eq 'f') { print PS "0 1 rlineto\n"; } elsif (\$ch eq 'F') { print PS "0 1 rmoveto\n"; } elsif (\$ch eq '+') { print PS "360 \$angle rotate\n"; } elsif (\$ch eq '-') { print PS "360 \$angle neg rotate\n"; } elsif (\$ch eq '!') { print PS "-1 1 scale\n"; } elsif (\$ch eq '[') { print PS "gsave\n"; } elsif (\$ch eq ']') { print PS "stroke\ngrestore\n"; } } print PS "stroke\nshowpage"; close PS; </code><p> Note that you need to replace uppercase F with lowercase f to turn on the 'pen'. 175816 175816